Methods for analyzing proportions

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2013-08

Authors

Moeller, Megan Michelle

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Abstract

The analysis of proportions is interesting and noteworthy in that there are no commonly accepted regression models for analyzing proportions; indeed, researchers most often use ordinary least squares to estimate the parameters of a linear regression model for proportional data. Such an approach, however, violates several assumptions of the Classical Linear Regression Model. This report outlines the general linear model and the problems associated with using this approach to model proportions and considers a variety of alternate approaches that researchers have taken to model proportions. These alternatives include transforming the dependent variable, a censored regression (Tobit) model, a Fractional Logit model, and Beta Regression. All of the approaches considered are implemented in a case study analyzing Rice party difference scores in the 93rd to 108th Congress. A comparison of the results from each approach confirms the findings of other researchers that Beta regression is the most preferred approach for modeling proportions.

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